FIG. 1 shows a lumped element model for a coil of wire. A coil of wire (or simple, “a coil”) is wiring that forms one or more loops as it progresses forward (e.g., a rectangular or circular spiral of wire). Coils are most often used for electronic components, such as inductors and transformers, that make use of magnetic fields. The lumped element model of FIG. 1 includes an inductor L that represents the inductance of the coil and a resistance R that represents the series resistance of the coil.
Both the inductance L and the resistance R increase as the number of windings (i.e., the number of loops) that the coil is comprised of increases. With respect to inductance, which is a metric related to the core's ability to store magnetic field energy, more windings corresponds to the creation of a greater magnetic field strength (and corresponding magnetic flux density) within the region encompassed by the coil's loops. With respect to resistance, which is a metric related to the amount of electrical energy that an electrical current will expend as it flows through the coil, more windings corresponds to a longer path that a current that flows through the coil must travel.
When a time varying current “i(t)” is driven through the coil, there will be a voltage drop across the entire coil VC=VL+VR where VL is the voltage drop across the inductive component L of the coil and VR is the voltage drop across the resistive component R of the coil. Here, VL=L(∂i(t)/∂t) and VR=i(t)R where L is the inductance of the coil, R is the resistance of the coil and (∂i(t)/∂t) is “the first derivative with respect to time” of the current i(t). The first derivative with respect to time of the current i(t) describes the rate of change of the current i(t) over time. As such, for example, if the current i(t) is a triangular waveform, the voltage drop over the inductive component of the coil VL will be a rectangular waveform (owing to the (∂i(t)/∂t) term).
Known techniques for measuring the current i(t) through a coil involves the addition of a small series resistance along the same current path that i(t) flows. The voltage drop across the small series resistance is measured and correlated to the coil current i(t). A problem, however, is that the measured voltage “signal” across the added series resistance is small because the added series resistance itself is small (e.g., to reduce the power consumption). Because the measured voltage signal is small, a voltage amplifier with large gain is used to help perform the overall correlation between the measured voltage and the coil current.
Unfortunately, voltage amplifiers with large gain have low bandwidth (owing to a amplifier characteristic known in the art as “gain-bandwidth product”). As such, the ability to accurately measure i(t) becomes less and less practicable as the time rate-of-change of i(t) increases. For example, if i(t) is an oscillating signal such as an oscillating sinusoid or triangular waveform, the ability to measure i(t) becomes less and less practicable with increasing frequency of oscillation.